Saving a loaded controller profile under a different name does not update the name correctly

[jn64]

Cemu version: latest b1c7058 + 9afae50 from #500
OS: Fedora 36

Description

When saving a loaded controller profile under a different name, the new name is used for the filename but is not updated in the <profile> tag.

Note: This is dependent on PR #500 but I think the bug exists before, it's just exposed to me now that I can load profiles.

After further testing, it doesn't need #500, can be reproduced from main branch.

Steps to reproduce

1. Create a profile with name foo
2. Save profile → controllerProfiles/foo.xml is created containing <profile>foo</profile>
3. With profile foo loaded, change the name to bar
4. Save profile → controllerProfiles/bar.xml is created, still containing <profile>foo</profile>

Suspected cause

Cemu/src/input/InputManager.cpp

Lines 475 to 477 in b1c7058

	if (emulated_controller->has_profile_name())
	emulated_controller_node.append_child("profile").append_child(pugi::node_pcdata).set_value(
	emulated_controller->get_profile_name().c_str());

When saving, it's getting the existing profile name to write to the <profile> tag?

[BParks21]

Yeah I experience this all the time It's annoying.